3.7. The role of internal dust
Until now we have omitted the solid component of nebulae, which, although not important by mass (usually of the order of 10-3, see Hoare et al. 1991, Natta & Panagia 1981, Stasinska & Szczerba 1999) importantly affects the properties of PNe and H II regions. The discussion below deals only with aspects that are explicitly linked with the derivation of the chemical composition of nebulae.
3.7.1. Evidence for the presence of dust in the ionized regions
Numerous mid- and far- IR spectral observations of PNe and H II regions have shown the presence of a strong continuous emission at a temperature around 100 - 200 K, attributed to dust grains heated by the ionizing stars (see the discussion in Pottasch 1984). Near- and mid-IR array observations have shown that the distribution of this emission is comparable to the distribution of [NeII] 12.8µm and [SIV] 10.5µm radiation, implying that dust is not only found in the neutral outskirts, but also inside the ionized regions (see review by Barlow 1993). This does not necessarily imply, however, that grains are intimately mixed with ionized gas. A priori, they could be located exclusively in tiny, dusty neutral clumps, such as observed in the Helix nebula NGC 7293 (e. g. O'Dell & Handron 1996) or in the Ring Nebula NGC 6720 (Garnett & Dinerstein 2001). A crucial piece of evidence is provided by the following argument. It has been demonstrated by Kingdon et al. (1995) and Kingdon & Ferland (1997) that, in nebulae of normal chemical composition, numerous lines of elements such as Mg, Al, Ca, Cr, Fe, should be detectable in ultraviolet or optical spectra. What observations show is that these elements are depleted in PNe by factors around 10 - 100 (Shields 1978, Shields et al. 1981, Shields 1983, Harrington & Marionni 1981, Volk et al. 1997, Perinotto et al. 1999, Casassus et al. 2000). The same holds for H II regions (Osterbrock et al. 1992, Esteban et al. 1998).
3.7.2. Heavy element depletion
One important consequence of the above mentioned observational fact is that analyses of ionized nebulae do not provide the real abundance of such elements as Mg, Al, Ca, Cr, Fe, which can be incorporated in grains. Carbon can also be significantly depleted in carbon-rich grains - graphite or PAHs. The measurement of carbon abundances from nebular lines therefore gives only a lower limit to the total carbon content. This is also true for oxygen, although to a much smaller extent. In H II regions it is possible to estimate the amount of oxygen trapped in dust grains from the observation of the Mg, Si and Fe depletions (see Esteban et al. 1998). Also, the consideration of the Ne/O ratio can be useful, since Ne, being a noble gas, cannot enter in the composition of grains.
3.7.3. The effect of dust on the ionization structure
Dust internal to H II regions and PNe competes with the gas in absorbing Lyman continuum photons, therefore lowering the H luminosity. The nebular ionization structure is affected by two competing processes. The ionization parameter drops due to the fact that part of the Lyman continuum photons are absorbed by dust and not by gas. This alone would tend to lower the general ionization level. The ionizing radiation field seen by the atomic species depends on the wavelength dependence of the dust absorption cross section. For conventional dust properties, the absorption cross section per H nucleon smootly decreases for energies above 13.6 eV (see e.g. Fig. 1 from Aanestad 1989), favouring the ionization of He with respect to H. In the model of the Orion nebula presented by Baldwin et al. (1991), the net effect of absorption by dust is to bring the H+ and He+ zones into closer agreement.
3.7.4. The effect of dust obscuration on the emission line spectrum
The presence of dust inside the ionized regions affects the emission line spectrum by selectively absorbing (and scattering) the emitted photons. Since the emission lines from various ions are formed in different zones, their relative fluxes as measured by the observer do not only depend on a general extinction law, but also on the differences in the geometrical paths of the photons in the different lines. This, in principle, can be modelled using a photoionization code including dust but the problem is complex and the solution extremely geometry-dependent. For practical purposes, as explained in Sect. 3.3, it is more convenient to deredden an observed spectrum by adjusting the observed Balmer decrement to a theoretical one. If comparisons need to be made with a photoionization model, then they should be made with the theoretical emitted spectrum without dust attenuation. Of course, such a procedure is only approximate.
Resonance lines have an increased path length with respect to other lines, and are therefore subject to stronger absorption by dust. This is the case of H Ly, which may be entirely trapped by grains in the case of very dusty nebulae (Ly absorption is actually one of the main heating agents of dust particles in planetary nebulae, see e.g. Pottasch 1984). Other resonance lines, such as C IV 1550, N V 1240 or Si IV 1400, are also affected by this selective absorption process. Usually, an escape probability formalism is used to account for it (Cohen et al. 1984). The observed intensity of the resonance lines depends on the amount of dust, on the ionization structure and on the velocity fields both in the nebula and in the surrounding halo and intervening interstellar medium (see e.g. Middlemass 1988). The inclusion of dust attenuation in a tailored photoionization model of the PN NGC 7662 results in a derived gas phase C abundance twice as large as would be deduced using classical methods (Harrington et al. 1982).
Another consequence of selective dust absorption is that it prevents the 100 % conversion of high-n Lyman lines into Ly and Balmer lines (the case B). For dusty environments such as the Orion Nebula, the H emissivity can be reduced by 15 % (Cota & Ferland 1988).
3.7.5. The effects of grains on heating and cooling of the gas
An obvious effect of the presence of grains on the thermal balance of ionized nebulae, is due to the depletion of strong coolants such as Si, Mg, Fe, which enhances the electron temperature with respect to a dust-free situation. This aspect is important not only for detailed model fitting of nebulae, but also when using grids of photoionization models to calibrate strong line methods for abundance determinations (Henry 1993, Shields & Kennicutt 1995).
Grains have also a direct influence on the energy balance. The photoelectric effect on dust grains has been shown by Spitzer (1948) to be a potential heating source in the interstellar matter. Baldwin et al. (1991) have introduced the physical effects of dust in the photoionization code CLOUDY. They constructed a detailed model of the Orion nebula and found that in this object, heating by photoelectric effect can amount to a significant proportion of the total heating while collisions of the gas particles with the grains contribute somewhat to the cooling.
The effect of dust heating is dramatic in the H-poor and extremely dusty planetary nebula IRAS 18333-2357 in which md / mH is estimated around 0.4 (Borkowski & Harrington 1991). In this object, heating is almost entirely due to photoelectric effect.
In nebulae in which dust-to-gas mass ratio, dust properties and grain size distributions have the canonical values, the relative importance of dust heating is generally not very large. If, however, there is a large proportion of small dust grains, then the contribution of dust heating to the total energy gains may become important, as demonstrated by Dopita & Sutherland (2000) on a grid of dusty photoionization models of planetary nebulae. The effect is more pronounced in the central parts of the nebulae, being proportional to the mean intensity of the ultraviolet radiation field, and gives rise to a strong temperature gradient.
If such small grains do exist (and there is now growing evidence for that (Weingartner & Draine, 2001), their presence in planetary nebulae would solve a number of problems that have found no satisfactory solution so far (see Stasinska & Szczerba 2001): i) the thermal energy deficit inferred in some objects from tailored photoionization modelling; ii) the large negative temperature gradients inferred directly from spatially resolved observations and indirectly from integrated spectra in some PNe; iii) the Balmer jump temperatures being systematically smaller than temperatures derived from forbidden lines; iv) the intensities of [OI] 6300 often observed to be larger than predicted by photoionization models: indeed, near the ionization front, Lyman continuum photons are exhausted and the only photons still present are photons below the Lyman limit. Those are not absorbed by hydrogen but can heat the gas via photoelectric effect on dust grains. One should however remember that dust is not the only way to enhance [OI] emission, other mechanisms have been mentioned in Sect. 1.1.
The energy gains per unit volume of gas due to photoelectric effect, Gd, are proportional to the number density of dust grains and to the intensity of the stellar radiation field. Combining with Eq. (1.16) which expresses the gains due to photoionization of hydrogen, GH, it is easy to show that Gd/GH is proportional to (md/mH)U, where U is the ionization parameter. This has important consequences in the case of filamentary structures. If small grains are present, the photoelectric effect will boost the electron temperature in the low density components. This will result in important small-scale temperature variations in the nebula. The models of Stasinska & Szczerba (2001) show that moderate density inhomogeneities (such as inferred from high resolution images of PNe) give rise to values of t2 similar to the ones obtained from observations. Note that, contrary to the dust-free case, the tenuous component has a higher Te than filaments or clumps, therefore the clumps are better confined.
Stasinska & Szczerba (2001) also point out that if, as expected, dielectronic recombinations for high level states strongly enhance the emissivities of recombination lines, the presence of small grains in filamentary planetary nebulae would boost the emission of recombination lines from the diffuse component, principally in the inner zone. Therefore, small grains could solve in a natural way both the temperature fluctuation problem and the ORL/CEL discrepancy.
The presence of small grains in planetary nebulae can be tested observationally by measuring the temperature in and between filaments.